Hamiltonian Cycles on Archimedean Solids Are Twisting Free

Richard Ehrenborg

doi:10.4169/amer.math.monthly.121.02.158

Hamiltonian Cycles on Archimedean Solids Are Twisting Free

American Mathematical Monthly ◽

10.4169/amer.math.monthly.121.02.158 ◽

2014 ◽

Vol 121 (2) ◽

pp. 158

Author(s):

Richard Ehrenborg

Keyword(s):

Hamiltonian Cycles ◽

Archimedean Solids

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A note on maximal hamiltonian cycles in the square of a graph

Demonstratio Mathematica ◽

10.1515/dema-1988-0419 ◽

1988 ◽

Vol 21 (4) ◽

pp. 1089-1093

Author(s):

Tomasz Traczyk

Keyword(s):

Hamiltonian Cycles ◽

Square Of A Graph

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Hamiltonicity of a class of toroidal graphs

Mathematica Slovaca ◽

10.1515/ms-2017-0367 ◽

2020 ◽

Vol 70 (2) ◽

pp. 497-503

Author(s):

Dipendu Maity ◽

Ashish Kumar Upadhyay

Keyword(s):

Connected Graph ◽

Hamiltonian Cycle ◽

Partial Solution ◽

The Other ◽

Hamiltonian Cycles ◽

The Face ◽

Toroidal Graphs

Abstract If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. There are eleven types of semi-equivelar maps on the torus. In 1972 Altshuler has presented a study of Hamiltonian cycles in semi-equivelar maps of three types {36}, {44} and {63} on the torus. In this article we study Hamiltonicity of semi-equivelar maps of the other eight types {33, 42}, {32, 41, 31, 41}, {31, 61, 31, 61}, {34, 61}, {41, 82}, {31, 122}, {41, 61, 121} and {31, 41, 61, 41} on the torus. This gives a partial solution to the well known Conjecture that every 4-connected graph on the torus has a Hamiltonian cycle.

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Hamiltonian Cycles in Strong Products of Graphs

Canadian Mathematical Bulletin ◽

10.4153/cmb-1979-037-0 ◽

1979 ◽

Vol 22 (3) ◽

pp. 305-309 ◽

Cited By ~ 5

Author(s):

J. C. Bermond ◽

A. Germa ◽

M. C. Heydemann

Keyword(s):

Connected Graph ◽

Hamiltonian Cycles ◽

Strong Product

Abstract. Let denote the graph (k times) where is the strong product of the two graphs G and H. In this paper we prove the conjecture of J. Zaks [3]: For every connected graph G with at least two vertices there exists an integer k = k(G) for which the graph is hamiltonian.

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